Power minimizing controller for a stage assembly

ABSTRACT

A method for moving a stage includes coupling a stage mover to the stage, and directing current to the stage mover with a control system. The stage mover includes a magnet array and a conductor array positioned adjacent to the magnet array. The conductor array includes a first layer of coils and a second layer of coils, with the first layer of coils being closer to the magnet array than the second layer of coils. The control system directs current to the first layer of coils and the second layer of coils independently. Further, the control system directs more current to the first layer of coils than the second layer of coils during a movement step to reduce the power consumption.

CROSS-REFERENCE TO RELATED APPLICATION

The present application is a continuation application and claims thebenefit under 35 U.S.C. 120 on co-pending U.S. patent application Ser.No. 14/505,852, filed on Oct. 3, 2014 and entitled “POWER MINIMIZINGCONTROLLER FOR A STAGE ASSEMBLY”. Additionally, U.S. patent applicationSer. No. 14/505,852 claims priority on U.S. Provisional Application Ser.No. 61/887,366 filed on Oct. 5, 2013 and entitled “POWER MINIMIZINGCONTROLLER”. As far as is permitted, the entire contents as disclosed inU.S. patent application Ser. No. 14/505,852 and U.S. ProvisionalApplication Ser. No. 61/887,366 are incorporated herein by reference.

BACKGROUND

Exposure apparatuses are commonly used to transfer images from a reticleonto a semiconductor wafer during semiconductor processing. A typicalexposure apparatus includes an illumination source, a reticle stageassembly that retains a reticle, a lens assembly, a wafer stage assemblythat retains a semiconductor wafer, a metrology system that monitors theposition of the stage assemblies, and a control system that controls thestage assemblies based on the position information from the metrologysystem. Typically, the wafer stage assembly includes a wafer stage base,a wafer stage that retains the wafer, and a wafer stage mover assemblythat precisely positions the wafer stage and the wafer. Somewhatsimilarly, the reticle stage assembly includes a reticle stage base, areticle stage that retains the reticle, and a reticle stage moverassembly that precisely positions the reticle stage and the reticle.

Unfortunately, the stage mover assemblies generate heat that canadversely influence the other components of the exposure apparatus. Forexample, the heat can distort certain components and/or adverselyinfluence the measurements taken by the metrology system.Conventionally, the stage mover assemblies are cooled by forcing acoolant around the movers of the stage mover assembly. However, it isoften very difficult to adequately or efficiently cool the stage moverassemblies. Accordingly, there is a never ending goal to improve theefficiency of the stage mover assemblies to reduce the amount of heatgenerated by the stage mover assemblies.

SUMMARY

The present invention is directed to a method for moving a stage thatincludes the steps of coupling a stage mover to the stage, and directingcurrent to the stage mover. The stage mover can include a magnet arrayand a conductor array positioned adjacent to the magnet array, theconductor array including a first layer of conductors (e.g. coils) and asecond layer of conductors (e.g. coils), wherein the first layer ofcoils is closer to the magnet array than the second layer of coils. Thepresent invention directs current to the first layer of coils and thesecond layer of coils independently with a control system. In certainembodiments, the control system directs more current to the first layerof coils than the second layer of coils during a movement step to reducethe power consumption.

As provided herein, the problem of minimizing the power losses (heatdissipation) in a stage mover that includes at least two layers of coilsis solved by an algorithm that provides the optimum ratio between thecurrents in the coil windings.

As non-exclusive examples, the stage mover can be a planar or a linearmotor.

The present invention is also directed to a stage mover assembly and anexposure apparatus.

BRIEF DESCRIPTION OF THE DRAWINGS

The novel features of this invention, as well as the invention itself,both as to its structure and its operation, will be best understood fromthe accompanying drawings, taken in conjunction with the accompanyingdescription, in which similar reference characters refer to similarparts, and in which:

FIG. 1 is a schematic illustration of an exposure apparatus havingfeatures of the present invention;

FIG. 2 is a perspective view of an embodiment of a stage assembly thatcan be included as part of the exposure apparatus of FIG. 1;

FIG. 3 is a graph that plots percent improvement in power loss versusacceleration for a stage assembly controlled pursuant to the presentinvention;

FIG. 4 is a graph that plots current versus acceleration for a stageassembly controlled pursuant to the present invention;

FIG. 5 is another graph that plots percent improvement in power lossversus acceleration for a stage assembly controlled pursuant to thepresent invention;

FIG. 6 is another graph that plots current versus acceleration for astage assembly controlled pursuant to the present invention;

FIG. 7 is yet another graph that plots percent improvement in power lossversus acceleration for a stage assembly controlled pursuant to thepresent invention;

FIG. 8 is yet another graph that plots current versus acceleration for astage assembly controlled pursuant to the present invention;

FIG. 9A is top plan view of a first embodiment of a first layer ofconductors and a second layer of conductors having features of thepresent invention;

FIG. 9B is an exploded perspective view of a first embodiment of a firstcoil unit and a second coil unit;

FIG. 10A is top plan view of another embodiment of a first layer ofconductors and a second layer of conductors having features of thepresent invention;

FIG. 10B is an exploded perspective view of another embodiment of afirst coil unit and a second coil unit;

FIG. 11 is a schematic illustration of a control system having featuresof the present invention;

FIG. 12 is a simplified side view of a mover assembly having features ofthe present invention;

FIG. 13 is an exploded perspective view of yet another embodiment of afirst coil unit and a second coil unit;

FIG. 14 is an exploded perspective view of still another embodiment of afirst coil unit and a second coil unit;

FIG. 15A is a simplified plan view of a magnet array having features ofthe present invention;

FIG. 15B is a simplified perspective view of a magnet having features ofthe present invention

FIG. 16 is a simplified side view of another embodiment of a moverassembly having features of the present invention; and

FIG. 17 is a simplified side view of a yet another embodiment of a moverassembly having features of the present invention.

DESCRIPTION

FIG. 1 is a schematic illustration of a precision assembly, namely anexposure apparatus 10 having features of the present invention. Theexposure apparatus 10 includes an apparatus frame 12, an illuminationsystem 14 (irradiation apparatus), an optical assembly 16 (lensassembly), a reticle stage assembly 18, a wafer stage assembly 20, ametrology (“measurement”) system 22, and a control system 24 (sometimesreferred to as a “controller”). The design of the components of theexposure apparatus 10 can be varied to suit the design requirements ofthe exposure apparatus 10.

A number of Figures include an orientation system that illustrates an Xaxis, a Y axis that is orthogonal to the X axis, and a Z axis that isorthogonal to the X and Y axes. It should be understood that theorientation system is merely for reference and can be varied. Forexample, the X axis can be switched with the Y axis and/or the exposureapparatus 10 can be rotated. Moreover, it should be noted that any ofthese axes can also be referred to as the first, second, and/or thirdaxes.

As an overview, the control system 24 is uniquely designed to controland drive one or both of the stage assemblies 18, 20 in a more efficientfashion. Stated in another fashion, the control system 24 controls thestage assemblies 18, 20 in a fashion that minimizes the amount ofresistive power loss. As a result thereof, less heat is generated andless power is consumed, and less cooling is required to maintain thetemperature of the stage assemblies 18, 20. Further, the control system24 provided herein is relatively simple to implement.

The exposure apparatus 10 is particularly useful as a lithographicdevice that transfers a pattern (not shown) of an integrated circuitfrom a reticle 26 onto a semiconductor wafer 28. The exposure apparatus10 mounts to a mounting base 30, e.g., the ground, a base, a floor orsome other supporting structure.

There are a number of different types of lithographic devices. Forexample, the exposure apparatus 10 can be used as a scanning typephotolithography system that exposes the pattern from the reticle 26onto the wafer 28 with the reticle 26 and the wafer 28 movingsynchronously. Alternatively, the exposure apparatus 10 can be astep-and-repeat type photolithography system that exposes the reticle 26while the reticle 26 and the wafer 28 are both stationary.

However, the use of the exposure apparatus 10 and stage assembliesprovided herein is not limited to a photolithography system forsemiconductor manufacturing. The exposure apparatus 10, for example, canbe used as an LCD photolithography system that exposes a liquid crystaldisplay device pattern onto a rectangular glass plate or aphotolithography system for manufacturing a thin film magnetic head.Further, the present invention can also be applied to a proximityphotolithography system that exposes a mask pattern by closely locatinga mask and a substrate without the use of a lens assembly. Additionally,the present invention provided herein can be used in other devices,including other semiconductor processing equipment, elevators, machinetools, metal cutting machines, inspection machines and disk drives.

The apparatus frame 12 is rigid and supports the components of theexposure apparatus 10. The design of the apparatus frame 12 can bevaried to suit the design requirements of the rest of the exposureapparatus 10. The apparatus frame 12 illustrated in FIG. 1 supports theoptical assembly 16, the reticle stage assembly 18, the wafer stageassembly 20, and the illumination system 14 above the mounting base 30.

The illumination system 14 includes an illumination source 32 and anillumination optical assembly 34. The illumination source 32 emits abeam (irradiation) of light energy. The illumination optical assembly 34guides the beam of light energy from the illumination source 32 to theoptical assembly 16. The beam of light energy selectively illuminatesdifferent portions of the reticle 26 and exposes the wafer 28.

The illumination source 32 can be a g-line source (436 nm), an i-linesource (365 nm), a KrF excimer laser (248 nm), an ArF excimer laser (193nm), a F₂ laser (157 nm), or an EUV source (13.5 nm). Alternatively, theillumination source 32 can generate charged particle beams such as anx-ray or an electron beam. For instance, in the case where an electronbeam is used, thermionic emission type lanthanum hexaboride (LaB₆) ortantalum (Ta) can be used as a cathode for an electron gun. Furthermore,in the case where an electron beam is used, the structure could be suchthat either a mask is used or a pattern can be directly formed on asubstrate without the use of a mask.

The optical assembly 16 projects and/or focuses the light passingthrough the reticle 26 to the wafer 28. Depending upon the design of theexposure apparatus 10, the optical assembly 16 can magnify or reduce theimage illuminated on the reticle 26. The optical assembly 16 need not belimited to a reduction system. It could also be a 1× or magnificationsystem.

The reticle stage assembly 18 holds and positions the reticle 26relative to the optical assembly 16 and the wafer 28. In FIG. 1, thereticle stage assembly 18 includes the reticle stage 18A that retainsthe reticle 26, and a reticle stage mover assembly 18B that positionsthe reticle stage 18A and the reticle 26. The reticle stage moverassembly 18B can be designed to move the reticle 26 along the X and Yaxes, and about the Z axis. Alternatively, the reticle stage moverassembly 18B can be designed to move the reticle 26 along the X, Y and Zaxes, and about the X, Y and Z axes.

Somewhat similarly, the wafer stage assembly 20 holds and positions thewafer 28 with respect to the projected image of the illuminated portionsof the reticle 26. In FIG. 1, the wafer stage assembly 20 includes thewafer stage 20A that retains the wafer 28, and a wafer stage moverassembly 20B that positions the wafer stage 20A and the wafer 28. Thewafer stage mover assembly 20B can be designed to move the wafer 28along the X and Y axes, and about the Z axis. Alternatively, the waferstage mover assembly 20B can be designed to move the wafer 28 along theX, Y and Z axes, and about the X, Y and Z axes.

The measurement system 22 monitors movement of the reticle 26 and thewafer 28 relative to the optical assembly 16 or some other reference.With this information, the control system 24 can control the reticlestage assembly 18 to precisely position the reticle 26 and the waferstage assembly 20 to precisely position the wafer 28. For example, themeasurement system 22 can utilize multiple laser interferometers,encoders, autofocus systems, and/or other measuring devices.

The control system 24 is electrically connected to the reticle stageassembly 18, the wafer stage assembly 20, and the measurement system 22.The control system 24 receives information from the measurement system22 and controls the stage assemblies 18, 20 to precisely position thereticle 26 and the wafer 28. The control system 24 can include one ormore processors and circuits.

As described above, a photolithography system according to the abovedescribed embodiments can be built by assembling various subsystems,including each element listed in the appended claims, in such a mannerthat prescribed mechanical accuracy, electrical accuracy, and opticalaccuracy are maintained. In order to maintain the various accuracies,prior to and following assembly, every optical system is adjusted toachieve its optical accuracy. Similarly, every mechanical system andevery electrical system are adjusted to achieve their respectivemechanical and electrical accuracies. The process of assembling eachsubsystem into a photolithography system includes mechanical interfaces,electrical circuit wiring connections and air pressure plumbingconnections between each subsystem. Needless to say, there is also aprocess where each subsystem is assembled prior to assembling aphotolithography system from the various subsystems. Once aphotolithography system is assembled using the various subsystems, atotal adjustment is performed to make sure that accuracy is maintainedin the complete photolithography system. Additionally, it is desirableto manufacture an exposure system in a clean room where the temperatureand cleanliness are controlled.

FIG. 2 is a perspective view of an embodiment of a stage assembly 236having features of the present invention. In various applications, thestage assembly 236 can be utilized as the reticle stage assembly 18and/or the wafer stage assembly 20 of the exposure apparatus 10illustrated above in FIG. 1. Alternatively, the stage assembly 236 canbe used for other types of usages.

As illustrated in this embodiment, the stage assembly 236 includes astage base 238, a stage 240 that retains a device 242, a stage mover 244(e.g. a planar motor), a countermass reaction assembly 246 (alsoreferred to herein simply as a “reaction assembly”), and a controlsystem 224. The design of each of these components can be varied to suitthe design requirements of the stage assembly 236.

In one embodiment, the stage mover 244 precisely moves the stage 240 andthe device 242 relative to the stage base 238 and the reaction assembly246. In some embodiments, the stage assembly 236 can further include atemperature controller (not illustrated) that controls the temperatureof the stage mover 244 and/or the reaction assembly 246 under thedirection of the control system 224.

The stage assembly 236 is particularly useful for precisely positioningthe device 242 during a manufacturing and/or an inspection process. Thetype of device 242 positioned and moved by the stage assembly 236 can bevaried. For example, the device 242 can be a semiconductor wafer, andthe stage assembly 236 can be used as part of the exposure apparatus 10for precisely positioning the semiconductor wafer during manufacturingof the semiconductor wafer.

Alternatively, for example, the stage assembly 236 can be used to moveother types of devices during manufacturing and/or inspection, to move adevice under an electron microscope (not shown), or to move a deviceduring a precision measurement operation (not shown).

The stage base 238 supports a portion of the stage assembly 236 abovethe mounting base 30 (illustrated in FIG. 1). In the embodimentillustrated herein, the stage base 238 is rigid and generallyrectangular shaped.

As noted above, the stage 240 retains the device 242. Further, the stage240 is precisely moved by the stage mover 244 to precisely position thedevice 242. In the embodiment illustrated herein, the stage 240 isgenerally rectangular shaped and includes a device holder (not shown)for retaining the device 242. The device holder can be a vacuum chuck,an electrostatic chuck, or some other type of clamp.

The stage 240 can be maintained spaced apart from (e.g., above) thereaction assembly 246 with the stage mover 244 if the stage mover 244 isa six degree of freedom mover that moves the stage 240 relative to thereaction assembly 246 with six degrees of freedom. In this embodiment,the stage mover 244 functions as a magnetic type bearing that levitatesthe stage 240. Alternatively, for example, the stage 240 can besupported relative to the reaction assembly 246 with a stage bearing(not shown), e.g., a vacuum preload type fluid bearing. For example, thebottom of the stage 240 can include a plurality of spaced apart fluidoutlets (not shown), and a plurality of spaced apart fluid inlets (notshown). In this example, pressurized fluid (not shown) can be releasedfrom the fluid outlets towards the reaction assembly 246 and a vacuumcan be pulled in the fluid inlets to create a vacuum preload type, fluidbearing between the stage 240 and the reaction assembly 246. In thisembodiment, the stage bearing allows for motion of the stage 240relative to the reaction assembly 246 along the X axis, along the Y axisand about the Z axis.

The stage mover 244 controls and adjusts the position of the stage 240and the device 242 relative to the reaction assembly 246 and the stagebase 238. For example, the stage mover 244 can be a planar motor thatmoves and positions the stage 240 along the X axis, along the Y axis andabout the Z axis (“three degrees of freedom” or “the planar degrees offreedom”). Further, in certain embodiments, the stage mover 244 can alsobe controlled to move the stage 240 along Z axis and about the X and Yaxes. With this design, the stage mover 244 is a six degree of freedommover.

In the embodiment illustrated in FIG. 2, the stage mover 244 includes aconductor array 250, and an adjacent magnet array 252 that interactswith the conductor array 250. In FIG. 2, the conductor array 250 iscoupled to the reaction assembly 246, and the magnet array 252 issecured to the stage 240 and is positioned above and adjacent to theconductor array 250. Alternatively, in another embodiment, the conductorarray 250 can be coupled to the stage 240 and the magnet array 252 canbe coupled to the reaction assembly 246. As provided herein, the arraysecured to the stage 240 can be referred to as the moving component (ormover) of the stage mover 244, and the array secured to the reactionassembly 246 can be referred to as the reaction component (or stator) ofthe stage mover 244.

In one embodiment, the conductor array 250 can include a plurality ofcoil units 254. The design and number of coil units 254 in the conductorarray 250 can vary according to the performance and movementrequirements of the stage mover 244. For example, in the embodimentillustrated in FIG. 2, the conductor array 250 includes one hundredeight coil units 254 that are arranged in a generally rectangulartwelve-by-nine array.

Further, in this embodiment, each conductor unit 254 includes an upper,first coil set 254A that includes one or more first coils (not shown inFIG. 2), and a lower, second coil set 254B that includes one or moresecond coils (not shown in FIG. 2). In this embodiment, for each coilunit 254, the first coil set 254A is closer to the magnet array 252 thanthe second coil set 254B. As a result thereof, for each coil unit 254,the first coil set 254A is positioned in a stronger magnetic field andhas a larger force constant than the corresponding second coil set 254B.

The first coil sets 254A collectively, can be referred to as an upper,first set (or layer) of conductors 256, and the second coil sets 254Bcollectively can be referred to as a lower, second set (or layer) ofconductors 258. Thus, (i) the upper, first layer of conductors 256 ispositioned closer to the magnet array 252 than the second layer ofconductors 258 along the Z axis, (ii) the first layer of conductors 256is positioned adjacent to the magnet array 252, (iii) the first layer ofconductors 256 is positioned between the magnet array 252 and the secondlayer of conductors 258, and (iv) the first layer of conductors 256 ispositioned in a stronger magnetic field and has a larger force constantthan the second layer of conductors 258.

The magnet array 252 can include one or more magnets (not illustrated inFIG. 2) that interact with the plurality of coil units 254. The designof the magnet array 252 and the number of magnets in the magnet array252 can be varied to suit the design requirements of the stage mover244. For example, for a planar motor, the magnet array 252 includes aplurality of magnets. In some embodiments, each magnet can be made of apermanent magnetic material such as NdFeB.

The reaction assembly 246 counteracts, reduces and/or minimizes theinfluence of the reaction forces from the stage mover 244 on theposition of the stage base 238 relative to the mounting base 30. Thisminimizes the distortion of the stage base 238 and improves thepositioning performance of the stage assembly 236. Further, for anexposure apparatus 10, this allows for more accurate positioning of thesemiconductor wafer.

As provided above, in the embodiment illustrated in FIG. 2, theconductor array 250 of the stage mover 244 is coupled to the reactionassembly 246. With this design, the reaction forces generated by thestage mover 244 are transferred to the reaction assembly 246. As aresult thereof, when the stage mover 244 applies a force to move thestage 240, an equal and opposite reaction force is applied to thereaction assembly 246.

In FIG. 2, the reaction assembly 246 is a generally rectangular shapedand can be maintained above the stage base 238 with a reaction bearing(not shown), e.g. a vacuum preload type fluid bearing. For example, thebottom of the reaction assembly 246 can include a plurality of spacedapart fluid outlets (not shown), and a plurality of spaced apart fluidinlets (not shown). Pressurized fluid (not shown) can be released fromthe fluid outlets towards the stage base 238 and a vacuum can be pulledin the fluid inlets to create a vacuum preload type, fluid bearingbetween the stage base 238 and the reaction assembly 246. In thisembodiment, the reaction bearing allows for motion of the reactionassembly 246 relative to the stage base 238 along the X axis, along theY axis and about the Z axis. Alternatively, for example, the reactionbearing can be a magnetic type bearing, or a roller bearing typeassembly.

With this design, through the principle of conservation of momentum, (i)movement of the stage 240 with the stage mover 244 along the X axis in afirst X direction along the X axis, generates an equal but opposite Xreaction force that moves the reaction assembly 246 in a second Xdirection that is opposite the first X direction along the X axis; (ii)movement of the stage 240 with the stage mover 244 along the Y axis in afirst Y direction, generates an equal but opposite Y reaction force thatmoves the reaction assembly 246 in a second Y direction that is oppositethe first Y direction along the Y axis; and (iii) rotation of the stage240 with the stage mover 244 about the Z axis in a first theta Zdirection, generates an equal but opposite theta Z reaction moment(torque) that rotates the reaction assembly 246 in a second theta Zdirection that is opposite the first theta Z direction about the Z axis.

The design of the reaction assembly 246 can be varied to suit the designrequirements of the stage assembly 236. In certain embodiments, theratio of the mass of the reaction assembly 246 to the mass of the stage240 is relatively high. This will minimize the movement of the reactionassembly 246 and minimize the required travel of the reaction assembly246. A suitable ratio of the mass of the reaction assembly 246 to themass of the stage 240 is between approximately 5:1 and 20:1. A largermass ratio is better, but is limited by the physical size of thereaction assembly 246.

Additionally, a trim mover (not shown) can be used to adjust theposition of the reaction assembly 246 relative to the stage base 238.For example, the trim mover can include one or more rotary motors, voicecoil motors, linear motors, electromagnetic actuators, or other type ofactuators.

In one embodiment, the control system 224 simultaneously andindependently directs a first current to the first layer of conductors256 and a second current to the second layer of conductors 258 toprecisely position the device 242. Stated in another fashion, duringeach movement step, the control system 224 independently controls thecurrents flowing through the layers of conductors 256, 258, and as such,the planar motor 244 can be considered to be composed of twoindependently controlled motors. Electrical current (not shown) suppliedto the coil units 254 interact with the magnetic field(s) of the one ormore magnets in the magnet array 252. This causes a force (Lorentz typeforce) between the coil units 254 and the magnets that can be used tomove the stage 240 relative to the stage base 238.

As provided herein, being closer to the magnet array 252, the top, firstset of conductors 256 has a first force constant K_(f) ^(T) that islarger than a second force constant K_(f) ^(B) of the bottom, second setof conductors 258 because the first set of conductors 256 are exposed toa stronger magnetic field than the bottom set of conductors 258. Sincethe first current directed to the first set of conductors 256 and thesecond current directed to the second set of conductors 258 can becontrolled independently with the control system 224, the presentinvention provides a method to determine what combination of currentvalues will result in the minimum amount of power consumption (and heatdissipation), and minimum overall power losses for each movement of thestage 240.

In certain embodiments, the control system 24 directs more current tothe first layer of conductors 256 than the second layer of conductors258 during each respective movement step to reduce the powerconsumption. As used herein, i^(T) represents the first current directedto the first layer of conductors 256, and i^(B) represents the secondcurrent directed to the second layer of conductors 258. In alternative,non-exclusive embodiments, for a given movement step, the control system24 directs at least approximately 1.03, 1.05, 1.1, 1.2, 1.5, 1.8, 2, or3 times more current to the first layer of conductors 256 than thesecond layer of conductors 258. Stated in another fashion, inalternative, non-exclusive embodiments, the control system 24 directsthe current so that the first current is at least approximately 3, 5,10, 20, 50, 100, or 200 percent greater than the second current.

It should be noted that for any given movement step, for the embodimentillustrated in FIG. 2, in certain embodiments, current is only directedto the particular coil sets 254A, 254B (or the particular coil units254) that are positioned in the magnetic fields of the magnet array 252.Thus, as the stage 240 is moved relative to the conductor array 250, theparticular coil units 254 that are energized will vary.

The difference in current amplitude to the sets of conductors 256, 258will vary according to the design of the stage mover 244. In certainembodiments, the difference between the current directed to the firstlayer of conductors 256 and the current directed to the second layer ofconductors 258 by the control system 224 can be expressed as a currentratio (“CR”), and can be expressed as follows:

$\begin{matrix}{{CR} = {\frac{I^{T}}{I^{B}}.}} & {{Equation}\mspace{14mu}(1)}\end{matrix}$

In alternative, non-exclusive embodiments, the current ratio is at leastapproximately 1.03, 1.05, 1.1, 1.2, 1.5, 1.8, 2, or 3. However, othervalues can be used.

As provided herein, to produce a certain, desired amount of force (F) onthe stage 240, the two layers of conductors 256, 258 must work togetheras follows:F=K _(f) ^(T) i ^(T) +K _(f) ^(B) i ^(B).  Equation (2)

The total power loss (“P”) corresponding to a single coil unit 254 canbe written asP=R ^(T) i ^(T) ² +R ^(B) i ^(B) ²   Equation (3),where R^(T) is the resistance of the first coil set 254A, and R^(B) isthe resistance of the second coil set 254B.

Thus, for a given value of force (F), there are infinitely manycombinations of i^(T) and i^(B) that would satisfy equation (2). Asprovided herein, there is a combination of the two current values thatwill result in the minimum amount of power consumption.

As a non-exclusive example, the stage assembly 236 can have thefollowing design parameter values: (i) mass (“m”) of the stage 240 ofseventy-five kilograms, (m=75 Kg); (ii) resistance of the first coil set254A and the second coil set 254B of four ohms (R^(T)=R^(B)=4.0 Ohms);(iii) the first layer of conductors 256 have a force constant oftwenty-five Newton per Ampere (K_(f) ^(T)=25.0N/A); and (iv) the secondlayer of conductors 258 have a force constant of twelve and one halfNewton per Ampere (K_(f) ^(B)=12.5N/A). In this example, the situationwhere the force (F) is solely used to accelerate the stage 240 with themass m is considered. Assuming in this simplified example that four coilunits 254 are utilized at any given time, the force produced by a singlecoil unit is expressed as F_(s)=(mg)/4, where F_(s) is the force for asingle coil unit, and g is the acceleration of the stage 240.

As provided herein, there is a combination of the two currents i^(T) andi^(B) that will result in the minimum amount of power consumption. Inone embodiment, to find the combination of currents that will result inthe minimum, Equation (3) is minimized subject to Equation (2). This canbe expressed as minimize P=R^(T)i^(T) ² +R^(B) i^(B) ² , subject toF=K_(f) ^(T)i^(T)+K_(f) ^(B) i^(B).

The solution to the above minimization problem is given by

$\begin{matrix}{{i^{B} = \frac{{FK}_{f}^{T}R^{B}}{{R^{T}K_{f}^{B^{2}}} + {R^{B}K_{f}^{T^{2}}}}}{and}} & {{Equation}\mspace{14mu}(4)} \\{i^{T} = {\frac{F - {K_{f}^{B}i^{B}}}{K_{f}^{T}}.}} & {{Equation}\mspace{14mu}(5)}\end{matrix}$

In other words, to produce a certain amount of force (F), usingequations (4) and (5), the best combination of the currents to thelayers of conductors 256, 258 (i^(T) and i^(B)) is found so that theoverall power consumption (from Equation (3)) is minimized. Solving forthe ratio of the currents in the top layer and the bottom layer coils(Equation 5 over Equation 4, or i^(T)/i^(B)), the following equationprovided the optimal current ratio which would result in the minimumpower consumption:

$\begin{matrix}{{CR} = {\frac{i^{T}}{i^{B}} = {\frac{R^{B}K_{f}^{T}}{R^{T}K_{f}^{B}}.}}} & {{Equation}\mspace{14mu}(6)}\end{matrix}$Thus, the optimal current ratio is equal to the ratio of (i) theresistance of the second layer of conductors multiplied by the firstforce constant, and (ii) the resistance of the first layer of conductorsmultiplied by the second force constant.

For stage assemblies in which the resistance of the first coil set 254Ais equal to the resistance of the second coil set 254B (R^(T)=R^(B)),Equation (6) can be reduced and rewritten as follows:

$\begin{matrix}{{CR} = {\frac{i^{T}}{i^{B}} = {\frac{K_{f}^{T}}{K_{f}^{B}}.}}} & {{Equation}\mspace{14mu}(7)}\end{matrix}$

Using Equation (7), the optimum current ratio for the example providedabove ((i) stage mass, m=75.0 Kg; (ii) R^(T)=R^(B)=4.0 Ohms; (iii) K_(f)^(T)=25.0N/A; and (iv) K_(f) ^(B)=12.5N/A is two (CR=2.0).

It should be noted that depending upon the design of the control system224, in certain embodiments, there is a maximum amount of current thatcan be sent to each layer of conductors. This maximum amount of currentcan also be referred to as the saturation level.

As provided herein, the percent improvement due to the Power MinimizingController, as defined by Equations (4)-(7), compared to a controlsystem that uses a current ratio of one (CR=1) can be determined usingthe following equation:

$\begin{matrix}{{\%\mspace{14mu}{Improvement}} = {{100 \times \left( {1 - \frac{P_{\min}}{P_{eq}}} \right)} = {100 \times {\left( {1 - \frac{R^{T}{R^{B}\left( {K_{f}^{T} + K_{f}^{B}} \right)}^{2}}{\left( {R^{T} + R^{B}} \right)\left( {{R^{T}K_{f}^{B^{2}}} + {R^{B}K_{f}^{T^{2}}}} \right)}} \right).}}}} & {{Equation}\mspace{14mu}(8)}\end{matrix}$In this equation, P_(min) represents the resistive power loss associatedwhen the stage mover is controlled to have improved performance (CR ‡1)as provided by the present invention; and P_(eq) represents theresistive power loss associated when the stage mover is controlled sothat the same current is directed to all of the layers of conductors(CR=1).

In Equation 8, in the example where the top, first layer of conductorsand the bottom, second layer of conductors are similar and have the sameresistance values, i.e. R^(T)=R^(B), Equation (8) can be rewritten asfollows:

$\begin{matrix}{{\%\mspace{14mu}{Improvement}} = {{100 \times \left( {1 - \frac{P_{\min}}{P_{eq}}} \right)} = {100 \times \left( {1 - {\frac{\left( {K_{f}^{T} + K_{f}^{B}} \right)^{2}}{2\left( {K_{f}^{B^{2}} + K_{f}^{T^{2}}} \right)}.}} \right.}}} & {{Equation}\mspace{14mu}(9)}\end{matrix}$

Using the parameters of the stage assembly provided above, andsubstituting these parameter values into Equation (9), or Equation (8),the improvement percent is ten (as provided above), when the currents tothe layers of conductors are below the saturation level.

In the case when the current to the top, first layer of conductorsreaches saturation, (i.e. i^(T)=i_(max)) for the general case, thefollowing equation can be used to calculate the amount of resistivepower loss (P_(min)) associated with the power minimizing controllerprovided herein:

$\begin{matrix}{P_{\min} = {{\left( \frac{R^{B}}{K_{f}^{B^{2}}} \right)F^{2}} - {\left( \frac{2\; R^{B}K_{f}^{R}i_{\max}}{K_{f}^{B^{2}}} \right)F} + {\left( \frac{{R^{T}K_{f}^{B^{2}}} + {R^{B}K_{f}^{T^{2}}}}{K_{f}^{B^{2}}} \right){i_{\max}^{2}.}}}} & {{Equation}\mspace{14mu}(10)}\end{matrix}$

The power loss (P_(eq)) associated with the controller using a unitycurrent ratio (CR=1), on the other hand, can be calculated by thefollowing equation:P _(eq)=(R ^(T) +R ^(B))i _(max) ².  Equation (11)

When both the first current to the top, first layer of conductors andthe second current to the bottom, second layer of conductors reach thesaturation level, equations (10) and (11) will result in the same amountof power consumption (P_(min)=P_(eq)).

As provided herein, some of the equations can be further simplifiedusing one or more dimensionless parameters. For example, anon-dimensional ratio of the force constants and a non-dimensional ratioof the resistance values can be used. As a non-exclusive example, thenon-dimensional ratio of the force constants, and the non-dimensionalratio of the resistance values can be defined as follows:

$\begin{matrix}{\alpha = \frac{K_{f}^{T}}{K_{f}^{B}}} & {{Equation}\mspace{14mu}(12)} \\{\beta = {\frac{R^{T}}{R^{B}}.}} & {{Equation}\mspace{14mu}(13)}\end{matrix}$In Equation 12, α is the non-dimensional ratio of the force constants.Similarly, in Equation 12, β is the non-dimensional ratio of theresistance values.

Using Equations 12 and 13, Equation (6) for the optimum current ratiocan be reduced to the following

$\begin{matrix}{\frac{i^{T}}{i^{B}} = {\frac{\alpha}{\beta}.}} & {{Equation}\mspace{14mu}(14)}\end{matrix}$

Somewhat similarly, Equation (8) can be rewritten as follows:

$\begin{matrix}{{\%\mspace{14mu}{Improvement}} = {{100 \times \left( {1 - \frac{P_{\min}}{P_{eq}}} \right)} = {100 \times \left( {1 - {\frac{{\beta\left( {1 + \alpha} \right)}^{2}}{\left( {1 + \beta} \right)\left( {\beta + \alpha^{2}} \right)}.}} \right.}}} & {{Equation}\mspace{14mu}(15)}\end{matrix}$

Further, for the example where the top, first layer of conductors andthe bottom, second layer of conductors are similar and have the sameresistance values, i.e. R^(T)=R^(B), then the non-dimensional ratio ofthe resistance values is equal to one (β=1), and Equation (15) can bereduced as follows:

$\begin{matrix}{{\%\mspace{14mu}{Improvement}} = {{100 \times \left( {1 - \frac{P_{\min}}{P_{eq}}} \right)} = {100 \times \left( {1 - {\frac{\left( {1 + \alpha} \right)^{2}}{2\left( {1 + \alpha^{2}} \right)}.}} \right.}}} & {{Equation}\mspace{14mu}(16)}\end{matrix}$

Using these Equations, for a simplified stage assembly having thecharacteristics of (i) a stage mass, m=75.0 Kg; (ii) R^(T)=R^(B)=4.0Ohms; (iii) K_(f) ^(T)=25.0N/A; and (iv) K_(f) ^(B)=12.5N/A), theoptimum current ratio is two (CR=2), and the percent improvement is ten(% improvement=10).

FIGS. 3-8 are alternative graphs that illustrate the improvement in theperformance for the stage assembly. The graphs in FIGS. 3-8 weregenerated using the stage assembly parameters provided in the previousparagraph.

More specifically, FIGS. 3 and 4 are graphs that show the results forthe case when there is no saturation limit for the currents (i^(T) andi^(B)) to the layers of conductors 256, 258. Stated in another fashion,in this example, unlimited current can be directed to the layers ofconductors 256, 258. FIG. 3 is a graph that includes a line 300 thatplots percent improvement in power loss versus acceleration andillustrates that the percent improvement in the total power loss with nosaturation limit for the currents is ten percent (10%) by adopting theoptimized current ratio, when compared to the controller which uses acurrent ratio of one (CR=1). FIG. 4 is the corresponding graph thatincludes (i) a solid line 400 that plots current versus acceleration forthe first layer of conductors with the optimized current ratio, (ii) along dashed line 402 that plots current versus acceleration for thesecond layer of conductors with the optimized current ratio; and (ii) ashort dashed line 404 that plots current versus acceleration for the twolayers of conductors when the current ratio is equal to one (equalcurrent is directed to each of the two layers of conductors). Asillustrated in FIG. 4, for the optimized current ratio, and becausethere is no saturation limit in this example, more current is alwaysdirected to the first layer of conductors than to the second layer ofconductors (compare line 400 to 402) to reach the desired acceleration.Further, for the non-optimized design, with the current ratio equal toone, the same current is directed to both layers of the conductors (line404) to reach the desired acceleration.

FIGS. 5 and 6 are graphs that show the results for the case when thereis a saturation limit of thirty amperes (30 Amps) for the currents(i^(T) and i^(B)) to the layers of conductors 256, 258. Stated inanother fashion, in this example, the maximum amount of current that canbe directed to each of the layers of conductors 256, 258 is thirtyamperes. FIG. 5 is a graph that includes a line 500 that plots percentimprovement in power loss versus acceleration and illustrates that thepercent improvement in the total power loss is ten percent (10%) whencompared to the controller which uses a current ratio of one (CR=1),until the current to the first layer of conductors reach the saturationpoint of thirty amperes. Subsequently, the percent improvement in thetotal power loss decreases from ten percent to zero at the point whereboth layers of conductors reach the saturation point.

FIG. 6 is the corresponding graph that includes (i) a solid line 600that plots current versus acceleration for the first layer of conductorswith the optimized current ratio, (ii) a long dashed line 602 that plotscurrent versus acceleration for the second layer of conductors with theoptimized current ratio; and (ii) a short dashed line 604 that plotscurrent versus acceleration for the two layers of conductors when thecurrent ratio is equal to one (equal current is directed to each of thetwo layers of conductors). As illustrated in FIG. 6, for the optimizedcurrent ratio, and because there is a saturation limit of thirty amperesin this example, more current is directed to the first layer ofconductors than to the second layer of conductors (compare line 600 to602) until the saturation limit is reached by both layers of conductorsto reach the desired acceleration. Further, for the non-optimizeddesign, with the current ratio equal to one, the same current isdirected to both layers of the conductors (line 604) to reach thedesired acceleration.

Somewhat similarly, FIGS. 7 and 8 are graphs that show the results forthe case when there is a saturation limit of twenty amperes (20 Amps)for the currents (i^(T) and i^(B)) to the layers of conductors 256, 258.Stated in another fashion, in this example, the maximum amount ofcurrent that can be directed to each of the layers of conductors 256,258 is twenty amperes. FIG. 7 is a graph that includes a line 700 thatplots percent improvement in power loss versus acceleration andillustrates that the percent improvement in the total power loss is tenpercent (10%) when compared to the controller which uses a current ratioof one (CR=1), until the current to the first layer of conductors reachthe saturation point of twenty amperes. Subsequently, the percentimprovement in the total power loss decreases from ten percent to zeroat the point where both layers of conductors reach the saturation point.

FIG. 8 is the corresponding graph that includes (i) a solid line 800that plots current versus acceleration for the first layer of conductorswith the optimized current ratio, (ii) a long dashed line 802 that plotscurrent versus acceleration for the second layer of conductors with theoptimized current ratio; and (ii) a short dashed line 804 that plotscurrent versus acceleration for the two layers of conductors when thecurrent ratio is equal to one (equal current is directed to each of thetwo layers of conductors). As illustrated in FIG. 8, for the optimizedcurrent ratio, and because there is a saturation limit of twenty amperesin this example, more current is directed to the first layer ofconductors than to the second layer of conductors (compare line 800 to802) until the saturation limit is reached by both layers of conductorsto reach the desired acceleration. Further, for the non-optimizeddesign, with the current ratio equal to one, the same current isdirected to both layers of the conductors (line 804) to reach thedesired acceleration.

It should be noted in these graphs that as the current in the upper, toplayer of conductors reaches saturation, the advantage of using the powerminimizing controller disclosed herein diminishes. Further, in theexamples provided herein, when the currents are below the saturationlevel, an improvement in the total power consumption of approximately10% can be achieved by utilizing the power minimizing controllerprovided herein, when compared to the case when the current ratio isone.

FIG. 9A is simplified, top plan view of a first embodiment of a firstlayer of conductors 956 and a second layer of conductors 958 of aconductor array 950. It should be noted that in FIG. 9A, the layers ofconductors 956, 958 are positioned side by side for clarity. In usage,the first layer of conductors 956 is stacked and positioned on top ofthe second layer of conductors 958 along the Z axis.

In this embodiment, the first layer of conductors 956 includes aplurality of X axis coil sets 960 and a plurality of Y axis coil sets962 that are arranged in an alternating fashion along the X axis andalong the Y axis. Stated in another fashion, the X axis coil sets 960are alternatively interspersed with the Y axis coil sets 962 along the Xaxis and along the Y axis to create a checkerboard pattern. Stated inyet another fashion, the first layer of conductors 956 illustrated inFIG. 9A is organized as a square grid that includes four rows (alignedwith the X axis), and four columns (aligned with the Y axis). Further,(i) in each row, the X axis coil sets 960 are alternatively interspersedwith the Y axis coil sets 962; and (ii) in each column, the X axis coilsets 960 are alternatively interspersed with the Y axis coil sets 962.Further, in certain embodiments, all of the coil sets 960, 962 in thefirst layer of conductors 956 are in substantially the same plane andhave the same Z axis position.

Similarly, in this embodiment, the second layer of conductors 958includes a plurality of X axis coil sets 960 and a plurality of Y axiscoil sets 962 that are arranged in an alternating fashion along the Xaxis and along the Y axis. Stated in another fashion, the X axis coilsets 960 are alternatively interspersed with the Y axis coil sets 962along the X axis and along the Y axis to create a checkerboard pattern.Further, in certain embodiments, all of the coil sets 960, 962 in thesecond layer of conductors 958 are in substantially the same plane andhave the same Z axis position.

It should be noted that either of the axis coil sets 960, 962 can bereferred as a first axis coil set or a second axis coil set.

Additionally, it should be noted that the number of coils sets 960, 962in each layer of conductors 956, 958 can be varied according to themovement requirements of the stage assembly 236 (illustrated in FIG. 2).In the simplified example in FIG. 9A, each layer of conductors 956, 958includes sixteen coil sets 960, 962. Alternatively, the conductor array950 can be designed to include more than sixteen or fewer than sixteencoil sets 956, 958.

With the design illustrated in FIG. 9A, in certain embodiments, thecontrol system 224 (illustrated in FIG. 2) can direct (i) current tocertain X axis coil sets 960 to create an interaction with the magneticfield(s) of the magnet array 252 (illustrated in FIG. 2) to generate oneor more X axis forces (not shown) along the X axis that are imparted onthe stage 240 (illustrated in FIG. 2), and (ii) current to certain Yaxis coil sets 962 to create an interaction with the magnetic field(s)of the magnet array 252 to generate one or more Y axis forces (notshown) along the Y axis that are imparted on the stage 240. Further, incertain embodiments, the control system 224 can directed (i) current tocertain X axis coil sets 960 to create an interaction with the magneticfield(s) of the magnet array 252 to generate one or more Z axis forces(not shown) along the Z axis that are imparted on the stage 240, and/or(ii) current to certain Y axis coil sets 962 to create an interactionwith the magnetic field(s) of the magnet array 252 to also generate oneor more Z axis forces. With this design, the X axis coil sets 960 areused to generate forces along the X and Z axes, and the Y axis coil sets962 are used to generate forces along the Y and Z axes. Further, incertain embodiments, multiple forces can be generated along each axis.These forces can be controlled to generate controllable forces about theX, Y, and Z axes.

It should also be noted that when the first layer of conductors 956 isstacked and positioned on top of the second layer of conductors 958, theconductor array 950 of FIG. 9A defines sixteen separate coil units (notshown in FIG. 9A) with each coil unit including one X axis coil set 960and one Y axis coil set 962. Further, these coil units can include (i)eight XY coil units, and (ii) eight YX coil units. In the XY coil units,the X axis coil set 960 (from the first layer of conductors 956) is ontop of the Y axis coil set 962 (from the second layer of conductors958). Further, in the YX coil units, the Y axis coil set 962 (from thefirst layer of conductors 956) is on top of the X axis coil set 960(from the second layer of conductors 958). Further, the XY coil unitsand the YX coil units are arranged in an alternating fashion along the Xaxis and along the Y axis.

FIG. 9B is an exploded perspective view of an XY coil unit 954XY and aYX coil unit 954YX from the conductor array 950 of FIG. 9A. In FIG. 9B,(i) for the XY coil unit 954XY, the X axis coil set 960 is positioned ontop of the Y axis coil set 962; and (ii) for the YX coil unit 954YX, theY axis coil set 962 is on top of the X axis coil set 960.

The design of each coil set 960, 962 can be varied. In FIG. 9B, eachcoil set 960, 962 includes three separate coils. Alternatively, eachcoil set 960, 962 can include more than three or fewer than three coils.Each coil can be a conductor that is made of a metal such as copper orany substance or material responsive to electrical current and capableof creating a magnetic field such as superconductors.

FIG. 10A is simplified, top plan view of another embodiment of a firstlayer of conductors 1056 and a second layer of conductors 1058 of aconductor array 1050. It should be noted that in FIG. 10A, the layers ofconductors 1056, 1058 are positioned side by side for clarity. In usage,the first layer of conductors 1056 is stacked and positioned on top ofthe second layer of conductors 1058 along the Z axis.

Similar to the embodiment illustrated in FIG. 9A, (i) the first layer ofconductors 1056 includes a plurality of X axis coil sets 1060 and aplurality of Y axis coil sets 1062 that are arranged in an alternatingfashion along the X axis and along the Y axis; (ii) the second layer ofconductors 1058 includes a plurality of X axis coil sets 1060 and aplurality of Y axis coil sets 1062 that are arranged in an alternatingfashion along the X axis and along the Y axis; and (iii) when the firstlayer of conductors 1056 is stacked and positioned on top of the secondlayer of conductors 1058, the conductor array 1050 of FIG. 10A definessixteen separate coil units (not shown in FIG. 10A).

However, in the embodiment illustrated in FIG. 10A, each coil unitincludes either two X axis coil sets 960 or two Y axis coil sets 962.Stated in another fashion, the conductor array 1050 defines (i) eight Xcoil units, and (ii) eight Y coil units. In the X coil units, one X axiscoil set 960 from the first layer of conductors 956) is on top of one Xaxis coil set 960 from the second layer of conductors 958. Further, inthe Y coil units, one Y axis coil set 962 from the first layer ofconductors 956 is on top of one Y axis coil set 962 from the secondlayer of conductors 958. Further, the X coil units and the Y coil unitsare arranged in an alternating fashion along the X axis and along the Yaxis.

FIG. 10B is an exploded perspective view of an X coil unit 1054X and a Ycoil unit 1054Y from the conductor array 1050 of FIG. 10A. In FIG. 10B,(i) for the X coil unit 1054X, the two X axis coil sets 1060 are stackedalong the Z axis; and (ii) for the Y coil unit 1054Y, the two Y axiscoil sets 1062 are stacked along the Z axis.

FIG. 11 is a control diagram that illustrates one embodiment of acontrol system 1148 having features of the present invention. In thisembodiment, moving left to right, the input block 1158 provides an inputsignal 1160, e.g., a position reference or trajectory control signalthat indicates a desired trajectory for a stage 1162. Next, the controlsystem 1148 receives a measurement signal 1164, provided by themeasurement system (illustrated in FIG. 1) that indicates a presentmeasured position of the stage 1162. The control system 1148 can use themeasurement signals 1164 to determine the current position and velocityof the stage 1162.

As further shown in FIG. 11, the input signal 1160, e.g., the desiredtrajectory, is combined with the measurement signal 1164 to form anerror signal 1166 that represents the difference between the measuredposition and the desired position. The error signal 1166 is subsequentlyinput to a controller 1168, which, in turn, generates a force commandand a torque command (indicated by single line 1169) for moving thestage 1162 as desired. Stated in another manner, the control system 1148via the controller 1168 generates the force command and the torquecommand based on the determined position and velocity information of thestage 1162, along with the desired trajectory of the stage 1162.

In certain embodiments, as shown, the force command and the torquecommand 1169 are sent to a commutator 1170, which uses the previouslydetermined current ratio for that stage mover (e.g. CR=2 for the exampleprovided above) to generate a first current command signal 1171A for theupper, first layer of conductors, and a second current command signal1171B for the lower, second layer of conductors of the stage mover.

The first current command signals 1171A generated by the commutator 1170are sent to a first drive module 1172A or amplifier for driving thephases 1174A (illustrated as a single phases) of the upper, first layerof conductors. The drive module 1172A then generates a first movercontrol signal 1175A for driving each phase 1174A of the upper, firstlayer of conductors to generate first layer forces 1180A that areapplied to the stage 1162.

Similarly, the second current command signals 1171B generated by thecommutator 1170 are sent to a second drive module 1172B or amplifier fordriving the phases 1174B (illustrated as a single phases) of the lower,second layer of conductors. The drive module 1172B then generates asecond mover control signal 1175B for driving each phase 1174B of thelower, second layer of conductors to generate second layer forces 1180Bthat are applied to the stage 1162.

Thus, in this embodiment, the first layer of conductors and the secondlayer of conductors function as two independently controlled motors, andthe current flowing to each layer of conductors is independentlycontrolled.

It should be noted that the present invention can be applied to othertypes of motors that use at least two redundant coils that areconfigured with a different force constant or resistance. For example,FIG. 12 is a simplified illustration of a portion of another embodimentof a control system 1224, and a stage assembly 1236 that includes astage mover 1244 that moves a stage 1240 relative to a stage base 1238primarily along an axis (e.g. the Y axis is this example). In thisembodiment, the stage mover 1244 is a linear motor that includes amagnet array 1252, and a conductor array 1250.

In this embodiment, the magnet array 1252 includes a plurality ofmagnets 1253 that are aligned in a one dimensional array. Further, theconductor array 1250 includes an upper, first layer of conductors 1256that are closer to the magnet array 1252, and a lower, second layer ofconductors 1258 that is farther away from the magnet array 1252. In thisdesign, the control system 1224 directs more current to the first layerof conductors 1256 than the second layer of conductors 1258.

Alternatively, for example, the present invention can be used in anothertype of mover, such as a voice coil motor.

Additionally, it should be noted that the present invention is alsouseful for conductor arrays that include more than two layers ofconductors. For example, FIG. 13 is an exploded perspective view ofanother embodiment of an XY coil unit 1354XY and a YX coil unit 1354YXthat can be used in a conductor array. In FIG. 13, (i) the XY coil unit1354XY includes two X axis coil sets 1360 that are positioned on the topand the bottom of one Y axis coil set 1362 along the Z axis; and (ii)the YX coil unit 1354YX includes two Y axis coil sets 1362 that arepositioned on the top and the bottom of one X axis coil set 1360 alongthe Z axis. With this design, the conductor array includes a first layerof conductors that is closest to the magnet array (not shown), a secondlayer of conductors that is next closest to the magnet array, and athird layer of conductors that is farthest from the magnet array.Further, for a given movement step, the control system (i) will directmore current to the first layer of conductors than the second layer ofconductors, and (ii) will direct more current to the second layer ofconductors than the third layer of conductors.

It should be noted that this design could be modified to include morethan three layers of conductors.

Somewhat similarly, FIG. 14 is an exploded perspective view of anotherembodiment of a X coil unit 1454X and a Y coil unit 1454Y that can beused in a conductor array. In FIG. 14, (i) the X coil unit 1454Xincludes three X axis coil sets 1460 that are stacked and aligned alongthe Z axis; and (ii) the Y coil unit 1454Y includes three Y axis coilsets 1462 that are stacked and aligned along the Z axis. With thisdesign, the conductor array includes a first layer of conductors that isclosest to the magnet array (not shown), a second layer of conductorsthat is next closest to the magnet array, and a third layer ofconductors that is farthest from the conductor array. Further, for agiven movement step, the control system (i) will direct more current tothe first layer of conductors than the second layer of conductors, and(ii) will direct more current to the second layer of conductors than thethird layer of conductors.

FIG. 15A is a simplified bottom plan view of a stage 1540 and a magnetarray 1552 that can be used with any of the conductor arrays (not shownin FIG. 15A) disclosed herein. In this, non-exclusive embodiment, themagnet array 1552 includes (i) two, spaced apart, X magnet sets 1552X,and (ii) two, spaced apart, Y magnet sets 1552Y that are secured to thebottom of the stage 1540. In this embodiment, (i) each of the X magnetsets 1552X interacts with fields generated by current in the X axis coilsets (not shown in FIG. 15A) to generate a separate X axis force; and(ii) each of the Y magnet sets 1552Y interacts with fields generated bycurrent in the Y axis coil sets (not shown in FIG. 15A) to generate aseparate Y axis force. Further, each of the X magnet sets 1552X includesa plurality of magnets 1553 that are spaced apart along the X axis, andeach of the Y magnet sets 1552Y includes a plurality of magnets 1553that are spaced apart along the Y axis.

FIG. 15B is a simplified perspective view of a magnet 1553 that can beused in the magnet array 1540 of FIG. 15A. In this embodiment, themagnet 1553 is a long, generally rectangular shaped.

FIG. 16 is a simplified illustration of a portion of yet anotherembodiment of a control system 1624, and a stage assembly 1636 thatincludes a stage mover 1644. In this embodiment, the stage mover 1644 isa linear motor that includes a magnet array 1652, and a conductor array1650.

Moreover, in this embodiment, the magnet array 1652 includes (i) a firstmagnet group 1652A that includes a plurality of magnets 1653 that arealigned in a one dimensional array; and (ii) a second magnet group 1652Bthat is spaced apart from the first magnet group 1652A and that includesa plurality of magnets 1653 that are aligned in a one dimensional array.

Further, the conductor array 1650 includes (i) an upper, first layer ofconductors 1656, (ii) a middle, second layer of conductors 1658, and(iii) a lower, third layer of conductors 1660. In this embodiment, (i)the first layer of conductors 1656 is closer to the first magnet group1652A than the second layer of conductors 1658, (ii) the second layer ofconductors 1658 is closer to the first magnet group 1652A than the thirdlayer of conductors 1660, (iii) the third layer of conductors 1660 iscloser to the second magnet group 1652B than the second layer ofconductors 1658, and (iv) the second layer of conductors 1658 is closerto the second magnet group 1652B than the first layer of conductors1656. In this embodiment, the control system 1624 directs a firstcurrent to the first layer of conductors 1656, a second current to thesecond layer of conductors 1658, and a third current to the third layerof conductors 1660. In certain embodiments, the first current and thethird current are greater than the second current during the movementstep to reduce the power consumption. Further, in certain embodiments,the first current is equal to the third current during a movement step.

FIG. 17 is a simplified illustration of a portion of yet anotherembodiment of a control system 1724, and a stage assembly 1736 thatincludes a stage mover 1744. In this embodiment, the stage mover 1744 isa voice coil motor that includes a magnet array 1752, and a conductorarray 1750.

Moreover, in this embodiment, the magnet array 1752 includes (i) a firstmagnet group 1752A that includes a plurality of magnets 1753; and (ii) asecond magnet group 1752B that is spaced apart from the first magnetgroup 1652A and that includes a plurality of magnets 1753.

Further, the conductor array 1750 includes (i) an upper, first layer ofconductors 1756, (ii) a middle, second layer of conductors 1758, and(iii) a lower, third layer of conductors 1760. In this embodiment, (i)the first layer of conductors 1756 is closer to the first magnet group1752A than the second layer of conductors 1758, (ii) the second layer ofconductors 1758 is closer to the first magnet group 1752A than the thirdlayer of conductors 1760, (iii) the third layer of conductors 1760 iscloser to the second magnet group 1752B than the second layer ofconductors 1758, and (iv) the second layer of conductors 1758 is closerto the second magnet group 1752B than the first layer of conductors1756. In this embodiment, the control system 1724 directs a firstcurrent to the first layer of conductors 1756, a second current to thesecond layer of conductors 1758, and a third current to the third layerof conductors 1760. In certain embodiments, the first current and thethird current are greater than the second current during the movementstep to reduce the power consumption. Further, in certain embodiments,the first current is equal to the third current during a movement step.

While a number of exemplary aspects and embodiments of the presentinvention have been discussed above, those of skill in the art willrecognize certain modifications, permutations, additions andsub-combinations thereof. It is therefore intended that the followingappended claims and claims hereafter introduced are interpreted toinclude all such modifications, permutations, additions andsub-combinations as are within their true spirit and scope.

What is claimed is:
 1. A method for moving a workpiece a movement step,the method comprising the steps of: coupling a stage mover to theworkpiece, the stage mover including (i) a magnet array including aplurality of magnets that are positioned substantially adjacent to oneanother; and (ii) a conductor array positioned adjacent to the magnetarray, the conductor array including a first layer of conductors and asecond layer of conductors that is adjacent to the first layer ofconductors, wherein the first layer of conductors is closer to themagnet array than the second layer of conductors, wherein the magnetarray is positioned on only one side of the conductor array, and whereina first force constant of the first layer of conductors is larger than asecond force constant of the second layer of conductors; and directingcurrent to the first layer of conductors and the second layer ofconductors independently with a control system, wherein the controlsystem simultaneously directs a first current to the first layer ofconductors and a second current to the second layer of conductors, andwherein the first current is greater than the second current during themovement step; and wherein the control system directs current so that acurrent ratio of the first current relative to the second current isgreater than one, and wherein the current ratio is approximately equalto the ratio of (i) a resistance of the second layer of conductorsmultiplied by the first force constant of the first layer of conductors,and (ii) a resistance of the first layer of conductors multiplied by thesecond force constant of the second layer of conductors.
 2. The methodof claim 1 wherein the first layer of conductors is positioned in astronger magnetic field than the second layer of conductors.
 3. Themethod of claim 1 wherein the step of directing includes directingcurrent so that the first current is at least approximately 1.2 timesgreater than the second current during the movement step.
 4. The methodof claim 1 wherein the step of directing includes directing current sothat the first current is at least approximately two times greater thanthe second current during the movement step.
 5. The method of claim 1wherein the step of directing includes using the current ratio todetermine the first current and the second current.
 6. The method ofclaim 1 wherein the step of coupling includes coupling one of a planarmotor, a linear motor and a voice coil motor to the workpiece.
 7. Themethod of claim 1 wherein the step of coupling includes the magnet arrayhaving one or more magnet groups, each of the magnet groups including aplurality of magnets that are positioned substantially adjacent to oneanother.
 8. A method for moving a workpiece a movement step, the methodcomprising the steps of: coupling a stage mover to the workpiece, thestage mover including (i) a magnet array including a plurality ofmagnets that are positioned substantially adjacent to one another; and(ii) a conductor array positioned adjacent to the magnet array, theconductor array including a first layer of conductors and a second layerof conductors that is adjacent to the first layer of conductors, whereina first force constant of the first layer of conductors is always largerthan a second force constant of the second layer of conductors;determining a current ratio of the first current relative to the secondcurrent using the first force constant of the first layer of conductorsand the second force constant of the second layer of conductors; anddirecting current to the first layer of conductors and the second layerof conductors independently with a control system, wherein the controlsystem simultaneously directs a first current to the first layer ofconductors and a second current to the second layer of conductors,wherein the first current is greater than the second current during themovement step, and wherein the current ratio is used to determine thefirst current and the second current; and wherein the control systemdirects current so that the current ratio of the first current relativeto the second current is greater than one, and wherein the current ratiois approximately equal to the ratio of (i) a resistance of the secondlayer of conductors multiplied by the first force constant of the firstlayer of conductors, and (ii) a resistance of the first layer ofconductors multiplied by the second force constant of the second layerof conductors.
 9. The method of claim 8 wherein the step of directingincludes directing current so that the first current is at leastapproximately 1.2 times greater than the second current during themovement step.
 10. The method of claim 8 wherein the step of directingincludes directing current so that the first current is at leastapproximately two times greater than the second current during themovement step.
 11. The method of claim 8 wherein the step of couplingincludes coupling one of a planar motor, a linear motor and a voice coilmotor to the workpiece.
 12. The method of claim 8 wherein the step ofcoupling includes the magnet array having one or more magnet groups,each of the magnet groups including a plurality of magnets that arepositioned substantially adjacent to one another.
 13. The method ofclaim 8 wherein the step of coupling includes the stage mover furthercomprising at least a third layer of conductors, wherein the third layerof conductors is further from the magnet array than the second layer ofconductors, and wherein the step of directing current includes thecontrol system also directing a third current to the third layer ofconductors, and wherein the second current is greater than the thirdcurrent during the movement step to reduce the power consumption.
 14. Amethod for moving a workpiece a movement step, the method comprising thesteps of: coupling a stage mover to the workpiece, the stage moverincluding (i) a magnet array including a plurality of magnets that arepositioned substantially adjacent to one another; and (ii) a conductorarray positioned adjacent to the magnet array, the conductor arrayincluding a first layer of conductors and a second layer of conductorsthat is adjacent to the first layer of conductors, wherein a first forceconstant of the first layer of conductors is larger than a second forceconstant of the second layer of conductors; determining a current ratioof the first current relative to the second current using the firstforce constant of the first layer of conductors and the second forceconstant of the second layer of conductors; and directing current to thefirst layer of conductors and the second layer of conductorsindependently with a control system, wherein the control systemsimultaneously directs a first current to the first layer of conductorsand a second current to the second layer of conductors, wherein thefirst current is greater than the second current during the movementstep, and wherein the current ratio is used to determine the firstcurrent and the second current; wherein the step of coupling includesthe magnet array including a first magnet group and a second magnetgroup that is spaced apart from the first magnet group; wherein thestage mover includes a third layer of conductors; wherein the firstlayer of conductors is closer to the first magnet group than the secondlayer of conductors, and the second layer of conductors is closer to thefirst magnet group than the third layer of conductors; wherein the thirdlayer of conductors is closer to the second magnet group than the secondlayer of conductors, and the second layer of conductors is closer to thesecond magnet group than the first layer of conductors; and wherein thestep of directing current includes the control system directing a thirdcurrent to the third layer of conductors, and wherein the third currentis greater than the second current during the movement step to reducethe power consumption.
 15. A stage assembly for moving a workpiece amovement step, the stage assembly comprising: a stage mover that iscoupled to the workpiece, the stage mover including (i) a magnet arrayincluding a plurality of magnets that are positioned substantiallyadjacent to one another; and (ii) a conductor array positioned adjacentto the magnet array, the conductor array including a first layer ofconductors and a second layer of conductors that is adjacent to thefirst layer of conductors, wherein the first layer of conductors iscloser to the magnet array than the second layer of conductors, whereinthe magnet array is positioned on only one side of the conductor array,and wherein a first force constant of the first layer of conductors islarger than a second force constant of the second layer of conductors;and a control system that directs current to the first layer ofconductors and the second layer of conductors independently, wherein thecontrol system simultaneously directs a first current to the first layerof conductors and a second current to the second layer of conductors,and wherein the first current is greater than the second current duringthe movement step; and wherein the control system directs current sothat a current ratio of the first current relative to the second currentis greater than one, and wherein the current ratio is approximatelyequal to the ratio of (i) a resistance of the second layer of conductorsmultiplied by the first force constant of the first layer of conductors,and (ii) a resistance of the first layer of conductors multiplied by thesecond force constant of the second layer of conductors.
 16. The stageassembly of claim 15 wherein the first layer of conductors is positionedin a stronger magnetic field than the second layer of conductors. 17.The stage assembly of claim 15 wherein the control system directscurrent so that the first current is at least approximately 1.2 timesgreater than the second current during the movement step.
 18. The stageassembly of claim 15 wherein the control system directs current so thatthe first current is at least approximately two times greater than thesecond current during the movement step.
 19. The stage assembly of claim15 wherein the stage mover is selected from the group that includes aplanar motor, a linear motor, and a voice coil motor.